Search results for: ordinary differential equations

Authors: Retno A. S. Lestari, Wahyudi B. Sediawan, Siti Syamsiah, Sarto

Abstract:

Sulfur-oxidizing bacteria were isolated and then grown on salak fruit seeds forming a biofilm on the surface. Their performances in sulfide removal were experimentally observed. In doing so, the salak fruit seeds containing biofilm were then used as packing material in a cylinder. Biogas obtained from biological treatment, which contains 27.95 ppm of hydrogen sulfide was flown through the packed bed. The hydrogen sulfide from the biogas was absorbed in the biofilm and then degraded by the microbes in the biofilm. The hydrogen sulfide concentrations at a various axial position and various times were analyzed. A set of simple kinetics model for the rate of the sulfide removal and the bacterial growth was proposed. Since the biofilm is very thin, the sulfide concentration in the Biofilm at a certain axial position is assumed to be uniform. The simultaneous ordinary differential equations obtained were then solved numerically using Runge-Kutta method. The values of the parameters were also obtained by curve-fitting. The accuracy of the model proposed was tested by comparing the calculation results using the model with the experimental data obtained. It turned out that the model proposed can describe the removal of sulfide liquid using bio-filter in the packed bed. The biofilter could remove 89,83 % of the hydrogen sulfide in the feed at 2.5 hr of operation and biogas flow rate of 30 L/hr.

Keywords: sulfur-oxidizing bacteria, salak fruit seeds, biofilm, packing material, biogas

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Authors: Clarinda Vitorino Nhangumbe, Fredericks Ebrahim, Betuel Canhanga

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The price of an option weather derivatives can be approximated as a solution of the two-dimensional convection-diffusion dominant partial differential equation derived from the Ornstein-Uhlenbeck process, where one variable represents the weather dynamics and the other variable represent the underlying weather index. With appropriate financial boundary conditions, the solution of the pricing equation is approximated using a nonstandard finite difference method. It is shown that the proposed numerical scheme preserves positivity as well as stability and consistency. In order to illustrate the accuracy of the method, the numerical results are compared with other methods. The model is tested for real weather data.

Keywords: nonstandard finite differences, Ornstein-Uhlenbeck process, partial differential equations approach, weather derivatives

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Authors: Katerina Kormusheva

Abstract:

Pricing plays a pivotal role in the marketing discipline as it directly influences consumer perceptions, purchase decisions, and overall market positioning of a product or service. This paper seeks to expand current knowledge in the area of discriminatory and differential pricing, a main area of marketing research. The methodology includes developing a framework and a model for determining how many price points to implement in differential pricing. We focus on choosing the levels of differentiation, derive a function form of the model framework proposed, and lastly, test it empirically with data from a large-scale marketing pricing experiment of services in telecommunications.

Keywords: marketing, differential pricing, price points, optimization

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Authors: K. Y. Tseng, C. Y. Wu

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This paper employs a heuristic algorithm to solve engineering problems including truss structure optimization and optimal chiller loading (OCL) problems. Two different type algorithms, real-valued differential evolution (DE) and modified binary differential evolution (MBDE), are successfully integrated and then can obtain better performance in solving engineering problems. In order to demonstrate the performance of the proposed algorithm, this study adopts each one testing case of truss structure optimization and OCL problems to compare the results of other heuristic optimization methods. The result indicates that the proposed algorithm can obtain similar or better solution in comparing with previous studies.

Keywords: differential evolution, Truss structure optimization, optimal chiller loading, modified binary differential evolution

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Authors: Peña A. Roland R., Lozano P. Jean P.

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The waterflooding process is an enhanced oil recovery (EOR) method that appears tremendously successful. This paper shows the importance of the role of the numerical modelling of waterflooding and how to provide a better description of the fluid flow during this process. The mathematical model is based on the mass conservation equations for the oil and water phases. Rock compressibility and capillary pressure equations are coupled to the mathematical model. For discretizing and linearizing the partial differential equations, we used the Finite Volume technique and the Newton-Raphson method, respectively. The results of three scenarios for waterflooding in porous media are shown. The first scenario was estimating the water saturation in the media without rock compressibility and without capillary pressure. The second scenario was estimating the front of the water considering the rock compressibility and capillary pressure. The third case is to compare different fronts of water saturation for three fluids viscosity ratios without and with rock compressibility and without and with capillary pressure. Results of the simulation indicate that the rock compressibility and the capillary pressure produce changes in the pressure profile and saturation profile during the displacement of the oil for the water.

Keywords: capillary pressure, numerical simulation, rock compressibility, two-phase flow

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Authors: Abhilash Sahu, Amit Priyadarshi

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In this paper, we will discuss the existence of weak solutions of the Kirchhoff type boundary value problem on the Sierpinski gasket. Where S denotes the Sierpinski gasket in R² and S₀ is the intrinsic boundary of the Sierpinski gasket. M: R → R is a positive function and h: S × R → R is a suitable function which is a part of our main equation. ∆p denotes the p-Laplacian, where p > 1. First of all, we will define a weak solution for our problem and then we will show the existence of at least two solutions for the above problem under suitable conditions. There is no well-known concept of a generalized derivative of a function on a fractal domain. Recently, the notion of differential operators such as the Laplacian and the p-Laplacian on fractal domains has been defined. We recall the result first then we will address the above problem. In view of literature, Laplacian and p-Laplacian equations are studied extensively on regular domains (open connected domains) in contrast to fractal domains. In fractal domains, people have studied Laplacian equations more than p-Laplacian probably because in that case, the corresponding function space is reflexive and many minimax theorems which work for regular domains is applicable there which is not the case for the p-Laplacian. This motivates us to study equations involving p-Laplacian on the Sierpinski gasket. Problems on fractal domains lead to nonlinear models such as reaction-diffusion equations on fractals, problems on elastic fractal media and fluid flow through fractal regions etc. We have studied the above p-Laplacian equations on the Sierpinski gasket using fibering map technique on the Nehari manifold. Many authors have studied the Laplacian and p-Laplacian equations on regular domains using this Nehari manifold technique. In general Euler functional associated with such a problem is Frechet or Gateaux differentiable. So, a critical point becomes a solution to the problem. Also, the function space they consider is reflexive and hence we can extract a weakly convergent subsequence from a bounded sequence. But in our case neither the Euler functional is differentiable nor the function space is known to be reflexive. Overcoming these issues we are still able to prove the existence of at least two solutions of the given equation.

Keywords: Euler functional, p-Laplacian, p-energy, Sierpinski gasket, weak solution

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Authors: Reza Mohammadi, Mahdieh Sahebi

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We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme.

Keywords: fourth-order parabolic equation, variable coefficient, polynomial quintic spline, off-step points, stability analysis

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Authors: Kamal, J. P. Narayan

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In the present wok the effects of basin-shape-ratio on the frequency content and spectral amplitudes of the basin-generated surface waves and the associated spatial variation of ground motion amplification and differential ground motion in a 3D semi-spherical basin has been studied. A recently developed 3D fourth-order spatial accurate time-domain finite-difference (FD) algorithm based on the parsimonious staggered-grid approximation of the 3D viscoelastic wave equations was used to estimate seismic responses. The simulated results demonstrated the increase of both the frequency content and the spectral amplitudes of the basin-generated surface waves and the duration of ground motion in the basin with the increase of shape-ratio of semi-spherical basin. An increase of the average spectral amplification (ASA), differential ground motion (DGM) and the average aggravation factor (AAF) towards the centre of the semi-spherical basin was obtained.

Keywords: 3D viscoelastic simulation, basin-generated surface waves, basin-shape-ratio effects, average spectral amplification, aggravation factors and differential ground motion

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Authors: Panwasn Mahalawalert

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The purposes of this research were analyzed differential item functioning and differential test functioning of SWUSAT aptitude test classification by sex variable. The data used in this research is the secondary data from Srinakharinwirot University Scholastic Aptitude Test 2013 (SWUSAT). SWUSAT test consists of four subjects. There are verbal ability test, number ability test, reasoning ability test and spatial ability test. The data analysis was analyzed in 2 steps. The first step was analyzing descriptive statistics. In the second step were analyzed differential item functioning (DIF) and differential test functioning (DTF) by using the DIFAS program. The research results were as follows: The results of DIF and DTF analysis for all 10 tests in year 2013. Gender was the characteristic that found DIF all 10 tests. The percentage of item number that found DIF is between 6.67% - 60%. There are 5 tests that most of items favors female group and 2 tests that most of items favors male group. There are 3 tests that the number of items favors female group equal favors male group. For Differential test functioning (DTF), there are 8 tests that have small level.

Keywords: aptitude test, differential item functioning, differential test functioning, educational measurement

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Authors: Edward J. Kansa, Pavel Holoborodko

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Continuously differentiable radial basis functions (RBFs) are meshfree, converge faster as the dimensionality increases, and is theoretically spectrally convergent. When implemented on current single and double precision computers, such RBFs can suffer from ill-conditioning because the systems of equations needed to be solved to find the expansion coefficients are full. However, the Advanpix extended precision software package allows computer mathematics to resemble asymptotically ideal Platonic mathematics. Additionally, full systems with extended precision execute faster graphical processors units and field-programmable gate arrays because no branching is needed. Sparse equation systems are fast for iterative solvers in a very limited number of cases.

Keywords: partial differential equations, Meshfree radial basis functions, , no restrictions on spatial dimensions, Extended arithmetic precision.

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Authors: Ruangdech Sirikit

Abstract:

The purposes of this study were analyzed differential item functioning and differential test functioning of SWUSAT aptitude test classification by sex variable. The data used in this research is the secondary data from Srinakharinwirot University Scholastic Aptitude Test 2011 (SWUSAT 2011) SWUSAT test consists of four subjects. There are verbal ability test, number ability test, reasoning ability test and spatial ability test. The data analysis was carried out in 2 steps. The first step was analyzing descriptive statistics. In the second step were analyzed differential item functioning (DIF) and differential test functioning (DTF) by using the DIFAS program. The research results were as follows: The results of data analysis for all 10 tests in year 2011. Sex was the characteristic that found DIF all 10 tests. The percentage of item number that found DIF was between 10% - 46.67%. There are 4 tests that most of items favors female group. There are 3 tests that most of items favors male group and there are 3 tests that the number of items favors female group equal favors male group. For Differential test functioning (DTF), there are 8 tests that have small DIF effect variance.

Keywords: differential item functioning, differential test functioning, SWUSAT, aptitude test

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Authors: Michael Fundator

Abstract:

Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA.

Keywords: Fokker-Plank stochastic differential equation, Kolmogorov-Chentsov continuity theorem, neural networks, translation and transcription

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Authors: Retno A. S. Lestari, Wahyudi B. Sediawan, Siti Syamsiah, Sarto

Abstract:

Sulfur-oxidizing bacteria were isolated and then grown on snakefruits seeds forming biofilm. Their performance in sulfide removal were experimentally observed. Snakefruit seeds were then used as packing material in a cylindrical tube. Biological treatment of hydrogen sulfide from biogas was investigated using biofilm on packed bed of snakefruits seeds. Biogas containing 27,9512 ppm of hydrogen sulfide was flown through the bed. Then the hydrogen sulfide concentrations in the outlet at various times were analyzed. A set of simple kinetics model for the rate of the sulfide removal and the bacterial growth was proposed. The axial sulfide concentration gradient in the flowing liquid are assumed to be steady-state. Mean while the biofilm grows on the surface of the seeds and the oxidation takes place in the biofilm. Since the biofilm is very thin, the sulfide concentration in the biofilm is assumed to be uniform. The simultaneous ordinary differential equations obtained were then solved numerically using Runge-Kutta method. The acuracy of the model proposed was tested by comparing the calcultion results using the model with the experimental data obtained. It turned out that the model proposed can be applied to describe the removal of sulfide liquid using bio-filter in packed bed. The values of the parameters were also obtained by curve-fitting. The biofilter could remove 89,83 % of the inlet of hydrogen sulfide from biogas for 2.5 h, and optimum loading of 8.33 ml/h.

Keywords: Sulfur-oxidizing bacteria, snakefruits seeds, biofilm, packing material, biogas

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Authors: N. R. Badurally Adam, S. R. Monebhurrun, M. Z. Dauhoo, A. Khoodaruth

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Transport energy demand is vital for the economic growth of any country. Globalisation and better standard of living plays an important role in transport energy demand. Recently, transport energy demand in Mauritius has increased significantly, thus leading to an abuse of natural resources and thereby contributing to global warming. Forecasting the transport energy demand is therefore important for controlling and managing the demand. In this paper, we develop a model to predict the transport energy demand. The model developed is based on a system of five stochastic differential equations (SDEs) consisting of five endogenous variables: fuel price, population, gross domestic product (GDP), number of vehicles and transport energy demand and three exogenous parameters: crude birth rate, crude death rate and labour force. An interval of seven years is used to avoid any falsification of result since Mauritius is a developing country. Data available for Mauritius from year 2003 up to 2009 are used to obtain the values of design variables by applying genetic algorithm. The model is verified and validated for 2010 to 2012 by substituting the values of coefficients obtained by GA in the model and using particle swarm optimisation (PSO) to predict the values of the exogenous parameters. This model will help to control the transport energy demand in Mauritius which will in turn foster Mauritius towards a pollution-free country and decrease our dependence on fossil fuels.

Keywords: genetic algorithm, modeling, particle swarm optimization, stochastic differential equations, transport energy demand

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Authors: Babak Safaei, A. M. Fattahi

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In the present study we have investigated axial buckling characteristics of nanocomposite beams reinforced by single-walled carbon nanotubes (SWCNTs). Various types of beam theories including Euler-Bernoulli beam theory, Timoshenko beam theory and Reddy beam theory were used to analyze the buckling behavior of carbon nanotube-reinforced composite beams. Generalized differential quadrature (GDQ) method was utilized to discretize the governing differential equations along with four commonly used boundary conditions. The material properties of the nanocomposite beams were obtained using molecular dynamic (MD) simulation corresponding to both short-(10,10) SWCNT and long-(10,10) SWCNT composites which were embedded by amorphous polyethylene matrix. Then the results obtained directly from MD simulations were matched with those calculated by the mixture rule to extract appropriate values of carbon nanotube efficiency parameters accounting for the scale-dependent material properties. The selected numerical results were presented to indicate the influences of nanotube volume fractions and end supports on the critical axial buckling loads of nanocomposite beams relevant to long- and short-nanotube composites.

Keywords: nanocomposites, molecular dynamics simulation, axial buckling, generalized differential quadrature (GDQ)

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Authors: Jyh-Yang Wu, Sheng-Gwo Chen

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In this paper, we present a simple effective numerical geometric method to estimate the divergence of a vector field over a curved surface. The conservation law is an important principle in physics and mathematics. However, many well-known numerical methods for solving diffusion equations do not obey conservation laws. Our presented method in this paper combines the divergence theorem with a generalized finite difference method and obeys the conservation law on discrete closed surfaces. We use the similar method to solve the Cahn-Hilliard equations on evolving spherical surfaces and observe stability results in our numerical simulations.

Keywords: conservation laws, diffusion equations, Cahn-Hilliard equations, evolving surfaces

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Authors: Alireza Rafie Boldaji, Ahmad Saboonchi

Abstract:

Chokes are commonly used in oil and gas production systems. A choke is a restriction basically designed to control flow rates of oil and gas wells, to prevent the downstream disturbances from propagating upstream (critical flow), and to protect the surface equipment facilities against slugging at high flowing pressures. There are different methods to calculate the multiphase flow rate, one of the multiphase flow measurement methods is the separation and measurement by on¬e-phaseFlow meter, another common method is the use of movable separator, their operations are very labor-intensive and costly. The current method used is based on the flow differential pressure on both sides of choke. Three groups of correlations describing two-phase flow through wellhead chokes were examined. The first group involved simple empirical equations similar to those of Gilbert, the second group comprised derived equations of two-phase flow incorporating PVT properties, and third group is computational method. In the article we calculate the flow of oil and gas through choke with simulation of this two phase flow bye computational fluid dynamic method, we use Ansys- fluent for this simulation and finally compared results of computational simulation whit empirical equations, the results show good agreement between experimental and numerical results.

Keywords: CFD, two-phase, choke, critical

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Authors: Gautam Kumar Saharia, Sagardeep Talukdar, Riki Dutta, Sudipta Nandy

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The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena.

Keywords: deep learning, optical Soliton, neural network, partial differential equation

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Authors: Pius W. Molo Chin

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Real life problems such as the Huxley equation are always modeled as nonlinear differential equations. These problems need accurate and reliable methods for their solutions. In this paper, we propose a nonstandard finite difference method in time and the Galerkin combined with the compactness method in the space variables. This coupled method, is used to analyze a two dimensional Huxley equation for the existence and uniqueness of the continuous solution of the problem in appropriate spaces to be defined. We proceed to design a numerical scheme consisting of the aforementioned method and show that the scheme is stable. We further show that the stable scheme converges with the rate which is optimal in both the L2 as well as the H1-norms. Furthermore, we show that the scheme replicates the decaying qualities of the exact solution. Numerical experiments are presented with the help of an example to justify the validity of the designed scheme.

Keywords: Huxley equations, non-standard finite difference method, Galerkin method, optimal rate of convergence

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Authors: Kholod Mohammad Abualnaja

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A new algorithm is presented to find some new iterative methods for solving nonlinear equations F(x)=0 by using the variational iteration method. The efficiency of the considered method is illustrated by example. The results show that the proposed iteration technique, without linearization or small perturbation, is very effective and convenient.

Keywords: variational iteration method, nonlinear equations, Lagrange multiplier, algorithms

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Authors: J. Liu, Z. P. Yu, L. Xiong, Y. Feng, J. He

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According to the independence, accuracy and controllability of the driving/braking torque of the distributed drive electric vehicle, a control strategy of differential drive assisted steering was designed. Firstly, the assisted curve under different speed and steering wheel torque was developed and the differential torques were distributed to the right and left front wheels. Then the steering return ability assisted control algorithm was designed. At last, the joint simulation was conducted by CarSim/Simulink. The result indicated: the differential drive assisted steering algorithm could provide enough steering drive-assisted under low speed and improve the steering portability. Along with the increase of the speed, the provided steering drive-assisted decreased. With the control algorithm, the steering stiffness of the steering system increased along with the increase of the speed, which ensures the driver’s road feeling. The control algorithm of differential drive assisted steering could avoid the understeer under low speed effectively.

Keywords: differential assisted steering, control strategy, distributed drive electric vehicle, driving/braking torque

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Authors: Ahmad Fahim Nasiry, Shigeo Honma

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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: numerical simulation, immiscible, finite difference, IADI, IDE, waterflooding

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Authors: Saghar Heidari

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In this paper, we study the valuation problem of European continuous-installment options under Markov-modulated models with a partial differential equation approach. Due to the opportunity for continuing or stopping to pay installments, the valuation problem under regime-switching models can be formulated as coupled partial differential equations (CPDE) with free boundary features. To value the installment options, we express the truncated CPDE as a linear complementarity problem (LCP), then a finite element method is proposed to solve the resulted variational inequality. Under some appropriate assumptions, we establish the stability of the method and illustrate some numerical results to examine the rate of convergence and accuracy of the proposed method for the pricing problem under the regime-switching model.

Keywords: continuous-installment option, European option, regime-switching model, finite element method

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Authors: Arin Ghazarian, Cyril Rakovski

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Differential privacy has become the leading technique to protect the privacy of individuals in a database while allowing useful analysis to be done and the results to be shared. It puts a guarantee on the amount of privacy loss in the worst-case scenario. Differential privacy is not a toggle between full privacy and zero privacy. It controls the tradeoff between the accuracy of the results and the privacy loss using a single key parameter called

Keywords: arrhythmia, cardiology, differential privacy, ECG, epsilon, medi-cal data, privacy preserving analytics, statistical databases

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Authors: Teng Li, Kamran Mohseni

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This paper presents an inviscid regularization technique that is capable of regularizing the shocks and sharp interfaces simultaneously in the shock-interface interaction simulations. The direct numerical simulation of flows involving shocks has been investigated for many years and a lot of numerical methods were developed to capture the shocks. However, most of these methods rely on the numerical dissipation to regularize the shocks. Moreover, in high Reynolds number flows, the nonlinear terms in hyperbolic Partial Differential Equations (PDE) dominates, constantly generating small scale features. This makes direct numerical simulation of shocks even harder. The same difficulty happens in two-phase flow with sharp interfaces where the nonlinear terms in the governing equations keep sharpening the interfaces to discontinuities. The main idea of the proposed technique is to average out the small scales that is below the resolution (observable scale) of the computational grid by filtering the convective velocity in the nonlinear terms in the governing PDE. This technique is named “observable method” and it results in a set of hyperbolic equations called observable equations, namely, observable Navier-Stokes or Euler equations. The observable method has been applied to the flow simulations involving shocks, turbulence, and two-phase flows, and the results are promising. In the current paper, the observable method is examined on the performance of regularizing shocks and interfaces at the same time in shock-interface interaction problems. Bubble-shock interactions and Richtmyer-Meshkov instability are particularly chosen to be studied. Observable Euler equations will be numerically solved with pseudo-spectral discretization in space and third order Total Variation Diminishing (TVD) Runge Kutta method in time. Results are presented and compared with existing publications. The interface acceleration and deformation and shock reflection are particularly examined.

Keywords: compressible flow simulation, inviscid regularization, Richtmyer-Meshkov instability, shock-bubble interactions.

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Authors: Mounir Belattar

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In this paper the Analysis of voltage waves that propagate along a lossless exponential nonuniform line is presented. For this analysis the parameters of this line are assumed to be varying function of the distance x along the line from the source end. The approach is based on the tow-port networks cascading presentation to derive the ABDC parameters of transmission using Picard-Carson Method which is a powerful method in getting a power series solution for distributed network because it is easy to calculate poles and zeros and solves differential equations such as telegrapher equations by an iterative sequence. So the impedance, admittance voltage and current along the line are expanded as a Taylor series in x/l where l is the total length of the line to obtain at the end, the main transmission line parameters such as voltage response and transmission and reflexion coefficients represented by scattering parameters in frequency domain.

Keywords: ABCD parameters, characteristic impedance exponential nonuniform transmission line, Picard-Carson's method, S parameters, Taylor's series

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Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

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The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: control, limits cycle, robot, stability

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Authors: Pranjal Srivastava, Piyali Sengupta

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The performance of marine drilling risers is crucial in the offshore oil and gas industry to ensure safe drilling operation with minimum downtime. Experimental investigations on marine drilling risers are limited in the literature owing to the expensive and exhaustive test setup required to replicate the realistic riser model and ocean environment in the laboratory. Therefore, this study presents an analytical model of marine drilling riser for determining its fragility under ocean environmental loading. In this study, the marine drilling riser is idealized as a continuous beam having a concentric circular cross-section. Hydrodynamic loading acting on the marine drilling riser is determined by Morison’s equations. By considering the equilibrium of forces on the marine drilling riser for the connected and normal drilling conditions, the governing partial differential equations in terms of independent variables z (depth) and t (time) are derived. Subsequently, the Runge Kutta method and Finite Difference Method are employed for solving the partial differential equations arising from the analytical model. The proposed analytical approach is successfully validated with respect to the experimental results from the literature. From the dynamic analysis results of the proposed analytical approach, the critical design parameters peak displacements, upper and lower flex joint rotations and von Mises stresses of marine drilling risers are determined. An extensive parametric study is conducted to explore the effects of top tension, drilling depth, ocean current speed and platform drift on the critical design parameters of the marine drilling riser. Thereafter, incremental dynamic analysis is performed to derive the fragility functions of shallow water and deep-water marine drilling risers under ocean environmental loading. The proposed methodology can also be adopted for downtime estimation of marine drilling risers incorporating the ranges of uncertainties associated with the ocean environment, especially at deep and ultra-deepwater.

Keywords: drilling riser, marine, analytical model, fragility

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Authors: Rabia Khan, Nargis Munir, Suriya Gharib, Syeda Roshana Ali

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In this paper linear equations are discussed in detail along with elimination method. Gaussian elimination and Gauss Jordan schemes are carried out to solve the linear system of equation. This paper comprises of matrix introduction, and the direct methods for linear equations. The goal of this research was to analyze different elimination techniques of linear equations and measure the performance of Gaussian elimination and Gauss Jordan method, in order to find their relative importance and advantage in the field of symbolic and numeric computation. The purpose of this research is to revise an introductory concept of linear equations, matrix theory and forms of Gaussian elimination through which the performance of Gauss Jordan and Gaussian elimination can be measured.

Keywords: direct, indirect, backward stage, forward stage

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Authors: Silas A. Ihedioha

Abstract:

In this work; it is considered that an investor’s portfolio is comprised of two assets; a risky stock which price process is driven by the geometric Brownian motion and a risk-free asset with Ornstein-Uhlenbeck Stochastic interest rate of return, where consumption, taxes, transaction costs and dividends are involved. This paper aimed at the optimization of the investor’s expected utility of consumption and terminal return on his investment at the terminal time having power utility preference. Using dynamic optimization procedure of maximum principle, a second order nonlinear partial differential equation (PDE) (the Hamilton-Jacobi-Bellman equation HJB) was obtained from which an ordinary differential equation (ODE) obtained via elimination of variables. The solution to the ODE gave the closed form solution of the investor’s problem. It was found the optimal investment in the risky asset is horizon dependent and a ratio of the total amount available for investment and the relative risk aversion coefficient.

Keywords: optimal, investment, Ornstein-Uhlenbeck, utility maximization, stochastic interest rate, maximum principle

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